Question

What is maximum number of rectangular components into which a vector can be split in its own plane

Answer 1

Two
In a plane you’re moving either in horizontal direction or vertical direction or both.

For e.g. you’re going upstairs. While going upstairs you’re moving horizontally forwards and vertically upwards. Your horizontal motion is the horizontal component of actual motion and your vertical motion is vertical component of actual motion.
Your motion is resolved into two components. No more components can be made in this 2D motion.